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- La ecuación:
-
Ecuación 3^x=7
-
Ecuación 2+3x=-7x-5
-
Ecuación 3-x/3=x/2
-
Ecuación 3/(x-5)+8/x=2
- Expresar {x} en función de y en la ecuación:
- -11*x-3*y=14
- -20*x-6*y=4
- 2*x-15*y=-1
- 8*x+3*y=4
-
Expresiones idénticas
- sin^(tres)(x)+ tres *sin(x)*cos(x)+sin(x)*cos(x)=5cos^(tres)(x)
- seno de en el grado (3)(x) más 3 multiplicar por seno de (x) multiplicar por coseno de (x) más seno de (x) multiplicar por coseno de (x) es igual a 5 coseno de en el grado (3)(x)
- seno de en el grado (tres)(x) más tres multiplicar por seno de (x) multiplicar por coseno de (x) más seno de (x) multiplicar por coseno de (x) es igual a 5 coseno de en el grado (tres)(x)
- sin(3)(x)+3*sin(x)*cos(x)+sin(x)*cos(x)=5cos(3)(x)
- sin3x+3*sinx*cosx+sinx*cosx=5cos3x
- sin^(3)(x)+3sin(x)cos(x)+sin(x)cos(x)=5cos^(3)(x)
- sin(3)(x)+3sin(x)cos(x)+sin(x)cos(x)=5cos(3)(x)
- sin3x+3sinxcosx+sinxcosx=5cos3x
- sin^3x+3sinxcosx+sinxcosx=5cos^3x
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Expresiones semejantes
- sin^(3)(x)+3*sin(x)*cos(x)-sin(x)*cos(x)=5cos^(3)(x)
- sin^(3)(x)-3*sin(x)*cos(x)+sin(x)*cos(x)=5cos^(3)(x)
- sin^(3)(x)+3*sinx*cosx+sinx*cosx=5cos^(3)(x)
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Expresiones con funciones
- Seno sin
- sin(2x)=0
- sin(x)^2=1/2
- sin(3*x)+sin(x)=0
- sin(x)=1/2
- sin((pi*x)/4)=-1
- Seno sin
- sin(2x)=0
- sin(x)^2=1/2
- sin(3*x)+sin(x)=0
- sin(x)=1/2
- sin((pi*x)/4)=-1
- Coseno cos
- cos(2*x-pi/4)=0
- cos(3*x+pi/4)=1
- cos(x^2)=1
- cos(x/8+pi/4)=1
- cos(x)=1
- Seno sin
- sin(2x)=0
- sin(x)^2=1/2
- sin(3*x)+sin(x)=0
- sin(x)=1/2
- sin((pi*x)/4)=-1
- Coseno cos
- cos(2*x-pi/4)=0
- cos(3*x+pi/4)=1
- cos(x^2)=1
- cos(x/8+pi/4)=1
- cos(x)=1
sin^(3)(x)+3*sin(x)*cos(x)+sin(x)*cos(x)=5cos^(3)(x) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 3 sin (x) + 3*sin(x)*cos(x) + sin(x)*cos(x) = 5*cos (x)
$$\left(\sin^{3}{\left(x \right)} + 3 \sin{\left(x \right)} \cos{\left(x \right)}\right) + \sin{\left(x \right)} \cos{\left(x \right)} = 5 \cos^{3}{\left(x \right)}$$
Suma y producto de raíces
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suma
/ / 6 5 4 3 2 \\ / / 6 5 4 3 2 \\ / / 6 5 4 3 2 \\ / / 6 5 4 3 2 \\ / / / 6 5 4 3 2 \\\ / / / 6 5 4 3 2 \\\ / / / 6 5 4 3 2 \\\ / / / 6 5 4 3 2 \\\ 2*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 0// + 2*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 1// + 2*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 2// + 2*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 3// + 2*re\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 4/// + 2*I*im\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 4/// + 2*re\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 5/// + 2*I*im\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 5///
$$\left(\left(\left(\left(2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 0\right)} \right)} + 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 1\right)} \right)}\right) + 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 2\right)} \right)}\right) + 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 3\right)} \right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 4\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 4\right)} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 5\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 5\right)} \right)}\right)}\right)$$
=
/ / 6 5 4 3 2 \\ / / 6 5 4 3 2 \\ / / 6 5 4 3 2 \\ / / 6 5 4 3 2 \\ / / / 6 5 4 3 2 \\\ / / / 6 5 4 3 2 \\\ / / / 6 5 4 3 2 \\\ / / / 6 5 4 3 2 \\\ 2*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 0// + 2*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 1// + 2*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 2// + 2*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 3// + 2*re\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 4/// + 2*re\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 5/// + 2*I*im\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 4/// + 2*I*im\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 5///
$$2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 0\right)} \right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 4\right)} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 5\right)} \right)}\right)} + 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 1\right)} \right)} + 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 2\right)} \right)} + 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 3\right)} \right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 4\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 5\right)} \right)}\right)}$$
producto
/ / 6 5 4 3 2 \\ / / 6 5 4 3 2 \\ / / 6 5 4 3 2 \\ / / 6 5 4 3 2 \\ / / / / 6 5 4 3 2 \\\ / / / 6 5 4 3 2 \\\\ / / / / 6 5 4 3 2 \\\ / / / 6 5 4 3 2 \\\\ 2*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 0//*2*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 1//*2*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 2//*2*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 3//*\2*re\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 4/// + 2*I*im\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 4////*\2*re\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 5/// + 2*I*im\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 5////
$$2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 0\right)} \right)} 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 1\right)} \right)} 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 2\right)} \right)} 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 3\right)} \right)} \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 4\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 4\right)} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 5\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 5\right)} \right)}\right)}\right)$$
=
/ / / / 6 5 4 3 2 \\\ / / / 6 5 4 3 2 \\\\ / / / / 6 5 4 3 2 \\\ / / / 6 5 4 3 2 \\\\ / / 6 5 4 3 2 \\ / / 6 5 4 3 2 \\ / / 6 5 4 3 2 \\ / / 6 5 4 3 2 \\ 64*\I*im\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 4/// + re\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 4////*\I*im\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 5/// + re\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 5////*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 0//*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 1//*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 2//*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 3//
$$64 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 4\right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 4\right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 5\right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 5\right)} \right)}\right)}\right) \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 0\right)} \right)} \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 1\right)} \right)} \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 2\right)} \right)} \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 3\right)} \right)}$$
64*(i*im(atan(CRootOf(5*x^6 - 8*x^5 - 15*x^4 + 8*x^3 + 15*x^2 + 8*x - 5, 4))) + re(atan(CRootOf(5*x^6 - 8*x^5 - 15*x^4 + 8*x^3 + 15*x^2 + 8*x - 5, 4))))*(i*im(atan(CRootOf(5*x^6 - 8*x^5 - 15*x^4 + 8*x^3 + 15*x^2 + 8*x - 5, 5))) + re(atan(CRootOf(5*x^6 - 8*x^5 - 15*x^4 + 8*x^3 + 15*x^2 + 8*x - 5, 5))))*atan(CRootOf(5*x^6 - 8*x^5 - 15*x^4 + 8*x^3 + 15*x^2 + 8*x - 5, 0))*atan(CRootOf(5*x^6 - 8*x^5 - 15*x^4 + 8*x^3 + 15*x^2 + 8*x - 5, 1))*atan(CRootOf(5*x^6 - 8*x^5 - 15*x^4 + 8*x^3 + 15*x^2 + 8*x - 5, 2))*atan(CRootOf(5*x^6 - 8*x^5 - 15*x^4 + 8*x^3 + 15*x^2 + 8*x - 5, 3))
Respuesta rápida
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/ / 6 5 4 3 2 \\ x1 = 2*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 0//
$$x_{1} = 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 0\right)} \right)}$$
/ / 6 5 4 3 2 \\ x2 = 2*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 1//
$$x_{2} = 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 1\right)} \right)}$$
/ / 6 5 4 3 2 \\ x3 = 2*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 2//
$$x_{3} = 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 2\right)} \right)}$$
/ / 6 5 4 3 2 \\ x4 = 2*atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 3//
$$x_{4} = 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 3\right)} \right)}$$
/ / / 6 5 4 3 2 \\\ / / / 6 5 4 3 2 \\\ x5 = 2*re\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 4/// + 2*I*im\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 4///
$$x_{5} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 4\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 4\right)} \right)}\right)}$$
/ / / 6 5 4 3 2 \\\ / / / 6 5 4 3 2 \\\ x6 = 2*re\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 5/// + 2*I*im\atan\CRootOf\5*x - 8*x - 15*x + 8*x + 15*x + 8*x - 5, 5///
$$x_{6} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 5\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(5 x^{6} - 8 x^{5} - 15 x^{4} + 8 x^{3} + 15 x^{2} + 8 x - 5, 5\right)} \right)}\right)}$$
Eq(x6, 2*re(atan(CRootOf(5*x^6 - 8*x^5 - 15*x^4 + 8*x^3 + 15*x^2 + 8*x - 5, 5))) + 2*i*im(atan(CRootOf(5*x^6 - 8*x^5 - 15*x^4 + 8*x^3 + 15*x^2 + 8*x - 5, 5))))
Respuesta numérica
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x1 = 2.32603759044697
x2 = -35.3730742526306
x3 = 14.3952277197381
x4 = 42.1863369026988
x5 = -5.58334449693477
x6 = 8.11204241255848
x7 = -91.9217420172468
x8 = 65.1578906622428
x9 = -98.2049273244264
x10 = -39.4950720906359
x11 = 90.2906318909612
x12 = 4.48722505962124
x13 = 33.7419641263449
x14 = -67.2861812735966
x15 = -1.79596024755835
x16 = -18.1497151112939
x17 = 88.664435110759
x18 = 58.3775248699952
x19 = 46.3083347407041
x20 = -77.1941839337134
x21 = 38.3989526533223
x22 = 69.8148791892203
x23 = -79.8525518879557
x24 = -41.6562595598101
x25 = 23.33678098116
x26 = 21.1755935119857
x27 = 25.8325820389632
x28 = 0.699840810244819
x29 = 98.735004667315
x30 = 71.4410759694224
x31 = -70.9109986265338
x32 = -64.6278133193542
x33 = -43.2824563400123
x34 = 61.0358928242375
x35 = -83.477369240893
x36 = 10.7704103668008
x37 = -29.587069430519
x38 = 79.8854487457763
x39 = -14.3623308619175
x40 = -10.2403330239122
x41 = 52.0943395628156
x42 = -26.9287014762767
x43 = -93.547938797449
x44 = 96.0766367130727
x45 = 102.359822020252
x46 = 44.6821379605019
x47 = -68.4151975687306
x48 = 48.4695222098783
x49 = -33.2118867834563
x50 = -52.061442704995
x51 = 64.6607101771748
x52 = 86.1686340529559
x53 = -62.132012261551
x54 = -49.5656416471919
x55 = -58.3446280121746
x56 = 17.0535956739804
x57 = -55.8488269543715
x58 = -89.7605545480726
x59 = -24.4329004184735
x60 = 27.4587788191653
x61 = 67.3190781314171
x62 = 54.7527075170579
x63 = -47.9394448669897
x64 = 84.0074465837816
x65 = 77.724261276602
x66 = -74.6983828759102
x67 = 40.0251494335245
x68 = 29.6199662883396
x69 = -11.8665298041144
x70 = 35.9031515955192
x71 = -99.8311241046286
x72 = -73.5693665807761
x73 = -60.5058154813489
x74 = 32.1157673461428
x75 = -20.6455161690971
x76 = 96.5738171981408
x77 = -54.2226301741693
x78 = 73.6022634385967
x79 = -16.5235183310918
x80 = -3.95714771673262
x81 = 92.4518193601354
x82 = -96.0437398552521
x83 = -45.7782573978155
x84 = 82.3812498035794
x85 = -87.2647534902694
x86 = 76.0980644963999
x87 = -35.8702547376986
x88 = -8.07914555473794
x89 = -86.1357371951353
x89 = -86.1357371951353